\begin{theindex} \item $D_n$ lattices, 840 \item $b_N$, 370 \item $c_N$, 370 \item $d_N$, 370 \item $e_N$, 370 \item $f_N$, 370 \item $g_N$, 370 \item $h_N$, 370 \item $i_N$, 370 \item $j_N$, 370 \item $k_N$, 370 \item $l_N$, 370 \item $m_N$, 370 \item $n_k$, 370 \item $r_N$, 370 \item $s_N$, 370 \item $t_N$, 370 \item $u_N$, 370 \item $v_N$, 370 \item $w_N$, 370 \item $x_N$, 370 \item $y_N$, 370 \item .gaprc, 912, 920, 927 \item {\tt /} for character tables, 779 \item 2-groups, 641 \item 3-groups, 643 \item 4.2BSD, 907 \item 4.3BSD, 907 \indexspace \item Abbreviating Section Names, 203 \item AbelianGroup, 630 \subitem for ag groups, 504 \item AbelianInvariants, 269 \subitem for ag groups, 503 \subitem for character tables, 778 \subitem for finitely presented groups, 462 \item AbelianInvariants for Ag Groups, 505 \item AbelianInvariantsNormalClosureFpGroup, 463 \item AbelianInvariantsNormalClosureFpGroupRrs, 463 \item AbelianInvariantsSubgroupFpGroup, 462 \item AbelianInvariantsSubgroupFpGroupMtc, 463 \item AbelianInvariantsSubgroupFpGroupRrs, 462 \item About Character Tables, 120 \item About Constants and Operators, 60 \item About Conventions, 58 \item About Defining New Domains, 150 \item About Defining New Group Elements, 162 \item About Defining New Parametrized Domains, 158 \item About Domains and Categories, 107 \item About Fields, 102 \item About Finitely Presented Groups and Presentations, 97 \item About First Steps, 59 \item About Functions, 64 \item About Further List Operations, 76 \item About GAP, 57 \item About Group Libraries, 135 \item About Groups, 81 \item About Help, 60 \item About Identical Lists, 67 \item About Lists, 65 \item About Loops, 74 \item About Mappings and Homomorphisms, 115 \item About Matrix Groups, 106 \item About Operations of Groups, 89 \item About Ranges, 73 \item About Records, 72 \item About Sets, 69 \item About Starting and Leaving GAP, 58 \item About Syntax Errors, 60 \item About the Implementation of Domains, 141 \item About Variables and Assignments, 62 \item About Vectors and Matrices, 70 \item About Writing Functions, 77 \item AbsInt, 346 \item absolute value of an integer, 346 \item AbstractGenerator, 452 \item AbstractGenerators, 452 \item accessing \subitem list elements, 555 \subitem record elements, 730 \item Accessing Record Elements, 730 \item Add, 558 \item add \subitem an element to a list, 558 \subitem an element to a set, 577 \subitem elements to a list, 558 \subitem the elements of a list, 571 \item AddBase, 340 \subitem for vector space, 340 \item AddedElementsCode, 1035 \item AddEdgeOrbit, 983 \item AddGenerator, 470 \item AddRelator, 470 \item AddSet, 577 \item Adjacency, 987 \item Advanced Methods for Dixon Schneider Calculations, 784 \item AffineOperation, 531 \item Ag Group Functions, 509 \item Ag Group Functions for Special Ag Groups, 551 \item Ag Group Operations, 498 \item Ag Group Records, 499 \item Ag Groups, 497 \item Ag Word Comparisons, 490 \item Ag Words, 489 \item Agemo, 256 \subitem for character tables, 778 \item AgGroup, 509 \subitem for Permutation Groups, 444 \item AgGroupFpGroup, 510 \item AgGroupQClass, 651 \item AgNormalizedAutomorphisms, 1092 \item AgNormalizedOuterAutomorphisms, 1092 \item AgOrbitStabilizer, 532 \item AgSubgroup, 521 \item Algebra, 664 \item Algebra Elements, 674 \item Algebra for MeatAxe Matrices, 1079 \item Algebra Functions for Algebras, 671 \item Algebra Functions for Matrix Algebras, 687 \item Algebra Homomorphisms, 673 \item Algebra Records, 675 \item Algebraic Extension Elements, 392 \item Algebraic Extension Records, 395 \item Algebraic extensions of fields, 391 \item Algebraic extensions of the Rationals, 395 \item AlgebraicExtension, 391 \item Algebras, 661 \item Algebras and Unital Algebras, 662 \item AllIrreducibleSolvableGroups, 645 \item AllPrimitiveGroups, 636 \item AllSolvableGroups, 640 \item AllThreeGroups, 643 \item AllTransitiveGroups, 638 \item AllTwoGroups, 641 \item Alpha, 892 \item AlternantCode, 1023 \item AlternatingGroup, 631 \item An example, 1003 \item An Example of a Computation in a Domain, 212 \item An Example of Advanced Dixon Schneider Calculations, 785 \item and, 726 \item AntiSymmetricParts, 825 \item ANU Pq, 965 \item ANU pq Package, 935 \item ANU Sq Package, 942 \item Append, 558 \item append \subitem elements to a list, 558 \subitem one string to another, 589 \subitem to a file, 206 \item AppendTo, 206 \item AreMOLS, 1068 \item Arrangements, 746 \item AsAlgebra, 667 \item AsGroup, 255 \subitem for ag groups, 504 \item AsGroup for Ag Groups, 504 \item AsModule, 694 \item assignment \subitem to a list, 556 \subitem to a record, 730 \subitem variable, 187 \item Assignments, 187 \item AssignVertexNames, 984 \item AssociatedPartition, 753 \item Associates, 229 \subitem for gaussians, 378 \item associativity, 186 \item AsSpace, 607 \item AsSpace for Modules, 694 \item AsSubalgebra, 667 \item AsSubgroup, 256 \item AsSubmodule, 694 \item AsSubspace, 606 \item AsUnitalAlgebra, 667 \item AsUnitalSubalgebra, 668 \item Atari ST, 922 \item ATLAS irrationalities, 370 \item ATLAS Tables, 868 \item atomic irrationalities, 370 \item augmented coset table, 471, 472 \item AugmentedCode, 1034 \item AutGroupGraph, 1002 \item automorphism group \subitem of a character table, 806 \subitem of a field, 242 \subitem of a matrix, 805 \subitem of an extension field, 393 \subitem of number fields, 386 \item AutomorphismGroup, 1052 \item AutomorphismGroupElements, 1094 \item Automorphisms, 1091 \subitem for character tables, 778 \item automorphisms \subitem of p groups, 970 \item Automorphisms of $p$-groups, 1091 \indexspace \item backslash, 587 \item Base, 339 \subitem of vector space, 339 \item base \subitem of a number field, 388 \subitem of vector space, 597 \item Base for MeatAxe Modules, 1083 \item Base for Permutation Groups, 437 \item BaseMat, 621 \item Bases for Matrix Algebras, 686 \item Basic Functions for Codes, 1042 \item Basis, 608 \item BCHCode, 1028 \item Bell, 744 \item BergerCondition, 893 \item Bernoulli, 755 \item BestKnownLinearCode, 1025 \item Bicomponents, 993 \item BinaryGolayCode, 1027 \item Binomial, 744 \item BipartiteDouble, 998 \item blank, 181 \item blist, 581 \item BlistList, 581 \item Blocks, 331 \subitem for Permutation Groups, 446 \item BlockSystemFlag, 1104 \item BNF, 193 \item body, 191 \item Boolean Lists, 581 \item Booleans, 725 \item bound, 183 \item Bounds \subitem Elias, 1060 \subitem Griesmer, 1061 \subitem Hamming, 1059 \subitem Johnson, 1060 \subitem Plotkin, 1060 \subitem Singleton, 1059 \subitem Sphere packing bound, 1059 \subitem UpperBound, 1061 \item Bounds on codes, 1058 \item BoundsMinimumDistance, 1063 \item Brauer Table Records, 775 \item Brauer tables \subitem format, 775 \item BrauerCharacterValue, 1080 \item BrauerTableOps, 778 \item Break Loops, 199 \item Browsing through the Sections, 202 \item Bruhat, 1137 \item BSD, 907 \indexspace \item CalcPres, 975 \item CallVE, 1116 \item candidates \subitem for permutation characters, 830 \item CanonicalAgWord, 493 \item CanonicalBasis, 608 \item Carmichaels lambda function, 356 \item Cartan matrices, 1131 \subitem direct sum of, 1131 \item CartanMat, 1131 \item Cartesian, 566 \item Cartesian product, 788 \item CAS Tables, 875 \item CAS tables,CAS format,CAS, 811 \item CentralCompositionSeriesPPermGroup, 440 \item Centralizer, 257 \subitem for ag groups, 501 \subitem for matrix groups, 626 \subitem for Permutation Groups, 441 \item CentralWeight, 491 \item Centre, 257 \subitem for character tables, 778 \item Centre for class functions, 883 \item CF, 383 \item Cgs, 521 \item ChangeCollector, 512 \item Changing Presentations, 469 \item Character, 885 \item character \subitem permutation, 279 \item character table \subitem display, 800 \item Character Table Libraries, 865 \item Character Table Records, 771 \item Character Tables, 769 \item character tables, 780, 865 \subitem access to, 780 \subitem ATLAS, 868 \subitem calculate, 780 \subitem CAS, 871, 875 \subitem computation, 784 \subitem conventions, 779 \subitem format, 771 \subitem generic, 813, 814, 816 \subitem libraries of, 865 \subitem of groups, 780 \subitem sort, 801, 803, 804 \item CharacterDegrees \subitem for character tables, 778 \item characteristic \subitem of a finite field element, 406 \item characteristic polynom \subitem of a field element, 243 \item CharacteristicPolynomial for MeatAxe matrices, 1079 \item Characters, 817 \item characters \subitem induce from cyclic subgroups, 828 \subitem induced, 828 \subitem inflated, 827 \subitem irreducible differences of, 826 \subitem permutation, 830 \subitem reduced, 822, 823 \subitem restricted, 827 \subitem scalar product of, 817, 818 \subitem sort, 801 \subitem symmetrisations of, 824, 825 \subitem tensor products of, 823 \item Characters of Finite Polycyclic Groups, 796 \item CharDegAgGroup, 794 \item CharFFE, 406 \item CharHeckeRepresentation, 1141 \item CharPol, 243 \item CharTable, 780 \item CharTableCollapsedClasses, 793 \item CharTableDirectProduct, 788 \item CharTableFactorGroup, 787 \item CharTableIsoclinic, 791 \item CharTableNormalSubgroup, 788 \item CharTableOps, 778 \item CharTablePGroup, 796 \item CharTableQClass, 652 \item CharTableRegular, 791 \item CharTableSpecialized, 816 \item CharTableSplitClasses, 792 \item CharTableSSGroup, 794 \item CharTableWreathSymmetric, 789 \item CheckFixedPoints, 856 \item CheckHeckeDefiningRelations, 1141 \item CheckMat, 1045 \item CheckMatCode, 1021 \item CheckPermChar, 855 \item CheckPol, 1046 \item CheckPolCode, 1027 \item chinese remainder, 347 \item ChineseRem, 347 \item ChooseRandomElements, 1105 \item ChopGMod, 1101 \item CHR, 974 \item Class Function Records, 890 \item Class Functions, 879 \item class functions, 845 \item class multiplication coefficient, 797, 798 \item class names, 797 \item classes \subitem collapse, 829 \subitem of cyclic subgroup, 799 \subitem real, 799 \subitem roots of, 799 \item ClassesNormalSubgroup, 890 \item ClassFunction, 884 \item ClassMultCoeffCharTable, 797 \item ClassNamesCharTable, 797 \item ClassNamesTom, 765 \item ClassOrbitCharTable, 799 \item ClassRootsCharTable, 799 \item ClassStructureCharTable, 798 \item ClassTypesTom, 765 \item clone \subitem an object, 739, 740 \item Closure, 258 \item Code Records, 1056 \item CodeIsomorphism, 1052 \item Codes, 1012 \item Codeword, 1006 \item CodewordNr, 1056 \item Codewords, 1006 \item coefficient \subitem binomial, 744 \item Coefficients, 342 \subitem in vector space, 342 \item coefficients \subitem for cyclotomics, 368 \item Coefficients for Number Fields, 388 \item Coefficients for Row Space Bases, 607 \item CoeffsCyc, 368 \item Cohomology, 973 \item CollapsedAdjacencyMat, 992 \item CollapsedCompleteOrbitsGraph, 999 \item CollapsedIndependentOrbitsGraph, 999 \item CollapsedMat, 829 \item Collected, 567 \item CollectorlessFactorGroup, 524 \item Combinations, 746 \item Combinatorics, 743 \item CombinatoricSplit, 784 \item Comm \subitem for group elements, 251 \subitem for words, 453 \item comments, 181 \item CommutativeDiagram, 848 \item CommutatorFactorGroup, 265 \subitem for finitely presented groups, 462 \item CommutatorSubgroup, 259 \subitem for ag groups, 501 \item CommutatorSubgroup for Ag Groups, 505 \item comparison \subitem of double cosets, 298 \subitem of right cosets, 294 \item Comparisons, 185 \item comparisons \subitem of booleans, 725 \subitem of finite field elements, 404 \subitem of integers, 344 \subitem of lists, 562 \subitem of polynomials, 414 \subitem of rationals, 363 \subitem of strings, 590 \item Comparisons of Booleans, 725 \item Comparisons of Codes, 1015 \item Comparisons of Codewords, 1008 \item Comparisons of Cyclotomics, 368 \item Comparisons of Domains, 214 \item Comparisons of Field Elements, 241 \item Comparisons of Finite Field Elements, 404 \item Comparisons of Gaussians, 375 \item Comparisons of Group Elements, 250 \item Comparisons of Integers, 344 \item Comparisons of Lists, 562 \item Comparisons of Mappings, 705 \item Comparisons of Permutations, 426 \item Comparisons of Polynomials, 414 \item Comparisons of Rationals, 363 \item Comparisons of Records, 733 \item Comparisons of Ring Elements, 225 \item Comparisons of Strings, 590 \item Comparisons of Unknowns, 401 \item Comparisons of Words, 453 \item Complement, 539 \item Complementclasses, 539 \item ComplementConjugatingAgWord, 540 \item ComplementGraph, 995 \item Complements, 539 \item CompleteGraph, 982 \item CompleteSubgraphs, 1001 \item CompleteSubgraphsOfGivenSize, 1001 \item Components of a $G$-module record, 1106 \item CompositionFactors for MeatAxe Modules, 1083 \item CompositionLength, 491 \item CompositionMapping, 714 \subitem for Frobenius automorphisms, 409 \subitem for GroupHomomorphismByImages, 311 \subitem for GroupHomomorphismByImages for permutation groups, 446 \item CompositionMaps, 846 \item CompositionSeries, 266 \subitem for Permutation Groups, 443 \item CompositionSubgroup, 525 \item Concatenation, 565 \item concatenation \subitem of lists, 565 \subitem of strings, 589 \item ConcatenationString, 589 \item conductor, 384 \item ConferenceCode, 1018 \item Congruences, 853 \item Conjugacy Class Records, 281 \item Conjugacy Classes, 279 \item ConjugacyClass, 280 \item ConjugacyClasses, 279 \subitem for ag groups, 503 \subitem for matrix groups, 626 \item ConjugacyClassesMaximalSubgroups, 290 \item ConjugacyClassesSubgroups, 282 \item ConjugacyClassSubgroups, 288 \item conjugate \subitem of a group, 312 \subitem of a group element, 250 \subitem of a word, 453 \item Conjugate Subgroup \subitem of Permutation Group, 441 \item Conjugates, 245 \subitem for finite fields, 410 \subitem for gaussians, 378 \item conjugates \subitem of a field element, Galois, 245 \item ConjugateSubgroup, 259 \subitem for ag groups, 501 \item ConjugateSubgroups, 292 \item ConjugationGroupHomomorphism, 308 \item ConnectedComponent, 992 \item ConnectedComponents, 993 \item ConsiderKernels, 854 \item ConsiderSmallerPowermaps, 854 \item ConsiderTableAutomorphisms, 857 \item ConstantWeightSubcode, 1039 \item Construction of Ag Groups, 498 \item Construction of Special Ag Groups, 547 \item ConstructionBCode, 1037 \item ContainedCharacters, 842 \item ContainedDecomposables, 841 \item ContainedMaps, 847 \item ContainedPossibleCharacters, 843 \item ContainedPossibleVirtualCharacters, 843 \item ContainedSpecialVectors, 842 \item Contents of the Table Libraries, 865 \item Conventions for Character Tables, 779 \item ConversionFieldCode, 1038 \item convert \subitem a finite field element to an integer, 407 \subitem to a list, 554 \subitem to a set, 576 \subitem to a string, 589 \subitem to an integer, 346 \item ConwayPolynomial, 419 \item CoprimeComplement, 540 \item Copy, 739 \item copy \subitem an object, 739, 740 \item Copyright of GAP for MS-DOS, 915 \item Copyright of GAP for TOS, 923 \item CordaroWagnerCode, 1024 \item Core, 259 \item CorrespondingAutomorphism, 1094 \item Coset, 293 \subitem for Permutation Groups, 442 \item coset \subitem double, 297, 298 \subitem left, 296 \subitem right, 293 \item CosetCode, 1038 \item Cosets \subitem for Permutation Groups, 442 \item cosets \subitem double, 297 \subitem left, 295 \subitem right, 292 \item Cosets of Subgroups, 292 \item CosetTableFpGroup, 464 \item CoveringGroup, 974 \item CoveringRadius, 1048 \item cross product of lists, 566 \item crystallographic groups, 647 \item Cycle, 319 \item CycleLength, 319 \item CycleLengths, 320 \item Cycles, 320 \item CyclicCodes, 1031 \item CyclicExtensionsTom, 765 \item CyclicGroup, 629 \subitem for ag groups, 504 \item CyclicGroup for Ag Groups, 506 \item cyclotomic field elements, 365 \item Cyclotomic Field Records, 383 \item Cyclotomic Integers, 366 \item CyclotomicCosets, 1070 \item CyclotomicPolynomial, 419 \item Cyclotomics, 365 \indexspace \item DadeGroup, 656 \item DadeGroupNumbersZClass, 656 \item data type \subitem unknown, 399 \item DEC, 818 \item Decode, 1053 \item DecodeTree, 485 \item DecomPoly, 396 \item DecomposedFixedPointVector, 761 \item DecomposedLeftCells, 1139 \item Decomposition, 818 \item decomposition \subitem of polynomials, 396 \item decomposition matrix, 818 \item DecompositionInt, 820 \item Decreased, 839 \item default field \subitem for cyclotomics, 384 \item default functions, 210 \item default ring \subitem for cyclotomic integers, 385 \item DefaultField, 240 \subitem for algebraic extensions, 394 \item DefaultField and Field for Cyclotomics, 384 \item DefaultRing, 224 \item DefaultRing and Ring for Cyclotomic Integers, 385 \item defect, 396 \item DefectApproximation, 396 \item Degree, 417 \item degree \subitem of a finite field element, 407 \item Degree for class functions, 883 \item DegreeFFE, 407 \item DegreeOperation, 323 \item Delta, 893 \item Denominator, 362 \item denominator \subitem of a rational, 362 \item Depth, 491 \item Derangements, 749 \item Derivative, 418 \item DerivedSeries, 265 \subitem for ag groups, 502 \item DerivedSubgroup, 260 \subitem for character tables, 778 \item Determinant for characters, 883 \item DeterminantMat, 619 \item DiagonalizeMat, 622 \item Diameter, 988 \item Difference, 219 \item difference \subitem of algebra elements, 674 \subitem of boolean lists, 584 \subitem of gaussians, 376 \subitem of list and algebra element, 674 \subitem of records, 735 \item DifferenceAgWord, 493 \item DifferenceBlist, 584 \item DihedralGroup, 630 \item Dimension, 341 \subitem of vector space, 341 \item dimension \subitem of vector space, 597 \item Dimension for MeatAxe Modules, 1083 \item Dimensions for MeatAxe matrices, 1079 \item DimensionsLoewyFactors, 269 \item DimensionsMat, 619 \item direct product, 788 \item DirectedEdges, 987 \item DirectProduct, 300 \subitem for ag groups, 504 \subitem for groups, 301 \item DirectProduct for Ag Groups, 507 \item DirectProduct for Groups, 301 \item DirectProductCode, 1041 \item DirectSumCartanMat, 1131 \item DirectSumCode, 1040 \item discrete logarithm \subitem of a finite field element, 408 \item dispatcher functions, 210 \item Dispatchers, 210 \item Display, 1055 \subitem for character tables, 778 \item Display for MeatAxe matrices, 1079 \item Display for MeatAxe Permutations, 1081 \item DisplayCharTable, 800 \item DisplayCrystalFamily, 648 \item DisplayCrystalSystem, 649 \item DisplayQClass, 650 \item DisplaySpaceGroupGenerators, 658 \item DisplaySpaceGroupType, 657 \item DisplayTom, 762 \item DisplayZClass, 653 \item Distance, 988 \item DistanceCodeword, 1011 \item DistanceGraph, 995 \item DistancesDistribution, 1050 \item DistanceSet, 993 \item DistanceSetInduced, 994 \item divisors \subitem of an integer, 352 \item DivisorsInt, 352 \item Dixon Schneider, 780 \item DixonInit, 784 \item DixonSplit, 784 \item DixontinI, 784 \item DnLattice, 840 \item DnLatticeIterative, 840 \item do, 190 \item Domain, 213 \item Domain Functions for Codes, 1043 \item Domain Functions for Number Fields, 389 \item domain record \subitem for right cosets, 295 \item Domain Records, 210 \item Domains, 209 \item Double Coset Records, 299 \item DoubleCoset, 297 \item DoubleCosetGroupOps, 298 \item DoubleCosets, 297 \item doublequotes, 587 \item DualCode, 1038 \item DualGMod, 1098 \item DualMatGroupSagGroup, 550 \indexspace \item E, 365 \item EB, 370 \item EC, 370 \item ED, 370 \item EdgeGraph, 996 \item EdgeOrbitsGraph, 981 \item Edit, 208 \item EE, 370 \item EF, 370 \item EG, 370 \item EH, 370 \item EI, 370 \item Eigenvalues, 821 \item EJ, 370 \item EK, 370 \item EL, 370 \item ElementAlgebra, 683 \item ElementaryAbelianGroup, 630 \subitem for ag groups, 504 \item ElementaryAbelianGroup for Ag Groups, 507 \item ElementaryAbelianSeries, 266 \subitem for ag groups, 502 \subitem for character tables, 778 \subitem for Permutation Groups, 443 \item ElementaryDivisorsMat, 622 \item ElementOfOrder, 1105 \item ElementOrdersPowermap, 862 \item ElementRowSpace, 610 \item Elements, 214 \subitem for ag groups, 499 \subitem for Conjugacy Classes, 281 \subitem for conjugacy classes of subgroups, 289 \subitem for double cosets, 298 \subitem for finite fields, 409 \subitem for finitely presented groups, 461 \subitem for groups, 311 \subitem for Permutation Groups, 441 \subitem for right cosets, 294 \subitem for vector spaces, 339 \item elements \subitem of a domain, 214 \item Elements for Ag Groups, 500 \item Elements for Groups, 311 \item Elements of Finitely Presented Algebras, 681 \item ElementsCode, 1017 \item ElementWithCharPol, 1105 \item elif, 188 \item EliminatedWord, 456 \item else, 188 \item EM, 370 \item Embedding \subitem into direct products, 300 \subitem into semidirect products, 301 \item embeddings of lattices, 836 \item end, 191 \item Enlarging Lists, 561 \item Environment, 197 \item environment, 191 \item equality \subitem for field homomorphisms, 247 \subitem of ag words, 490 \subitem of algebra elements, 674 \subitem of gaussians, 375 \subitem of group elements, 250 \subitem of group homomorphisms, 306 \subitem of records, 733 \item ER, 370 \item Error, 199 \item errors \subitem syntax, 197 \item ES, 370 \item ET, 370 \item EU, 370 \item EuclideanDegree, 231 \subitem for gaussians, 378 \subitem for polynomials, 421, 423 \item EuclideanQuotient, 232 \subitem for gaussians, 378 \subitem for polynomials, 421 \item EuclideanRemainder, 231 \subitem for gaussians, 378 \subitem for polynomials, 421 \item EulerianFunction, 270 \item Eulers totient function, 356 \item EV, 370 \item evaluation, 182 \item EvenWeightSubcode, 1033 \item EW, 370 \item EX, 370 \item Example Functions, 633 \item Example, normal closure, 541 \item Examples, 1108 \item Examples of Generic Character Tables, 814 \item Examples of the ATLAS format for GAP tables, 871 \item Examples of Vector Enumeration, 1118 \item Exec, 208 \item execution, 186 \item Exponent, 270 \subitem for character tables, 778 \item exponent \subitem of the prime residue group, 356 \item ExponentAgWord, 495 \item Exponents, 530 \item ExponentsAgWord, 495 \item ExponentsPermSolvablePermGroup, 444 \item ExponentSumWord, 455 \item Expressions, 182 \item ExpurgatedCode, 1034 \item ExtendedBinaryGolayCode, 1022 \item ExtendedCode, 1032 \item ExtendedIntersectionSumAgGroup, 533 \item ExtendedTernaryGolayCode, 1023 \item ExtendStabChain, 436 \item Extension Element Records, 395 \item ExtensionAutomorphism, 394 \item Extract, 838 \item Extraction Functions, 634 \item ExtraSpecialDecomp, 1103 \item EY, 370 \indexspace \item factor group \subitem table of, 787 \item Factor Groups of Ag Groups, 523 \item FactorArg, 524 \item FactorGroup, 263 \subitem for ag groups, 524 \item FactorGroup for AgGroups, 524 \item FactorGroupElement, 264 \item FactorGroupNormalSubgroupClasses, 890 \item Factorial, 743 \item Factorization, 270 \item factorization \subitem of an integer, 352 \item Factorization for PQp, 517 \item Factors, 230 \subitem for gaussians, 378 \subitem for polynomials, 422, 424 \item FactorsAgGroup, 530 \item FactorsInt, 352 \item Faithful Permutation Characters, 833 \item features \subitem under MS-DOS, 920 \subitem under TOS, 927 \subitem under UNIX, 912 \item Features of GAP for MS-DOS, 920 \item Features of GAP for TOS, 927 \item Features of GAP for UNIX, 912 \item FFList, 676 \item fi, 188 \item Fibonacci, 754 \item Field, 240 \subitem for algebraic extensions, 394 \item field \subitem cyclotomic, 383 \subitem finite, 403 \subitem for cyclotomics, 384 \subitem galois, 403 \subitem number, 382 \item Field Extensions, 391 \item Field functions for Algebraic Extensions, 394 \item Field Functions for Finite Fields, 410 \item Field Functions for Gaussian Rationals, 378 \item Field Functions for Rationals, 364 \item Field Homomorphisms, 246 \item field homomorphisms \subitem Frobenius, 409 \subitem of algebraic extensions, 394 \item Field Records, 248 \item FieldGenCentMat, 1100 \item Fields, 239 \item Fields over Subfields, 241 \item file \subitem append to a, 206 \subitem load a, 204 \subitem load a library, 205 \subitem log input to a, 206 \subitem log to a, 206 \subitem print to a, 205 \subitem read a, 204 \subitem read a library, 205 \item FileNameCharTable, 878 \item Filtered, 568 \item find \subitem an element in a list, 563 \subitem an element in a sorted list, 564 \item Fingerprint, 688 \item Fingerprint for MeatAxe Matrix Algebras, 1082 \item Finite Field Elements, 403 \item Finite Fields, 403 \item Finite Polycyclic Groups, 497 \item Finitely Presented Algebras, 677 \item Finitely Presented Groups, 459 \item finiteness test \subitem for domains, 216 \item FireCode, 1030 \item First, 569 \item FirstClassPQp, 516 \item FirstCohomologyDimension, 974 \item FirstNameCharTable, 878 \item FittingSubgroup, 260 \subitem for character tables, 778 \item FixedSubmodule, 697 \item Flat, 565 \item For, 190 \item for, 190 \item for loop, 190 \item ForAll, 568 \item ForAny, 569 \item Format of Sections, 201 \item FpAlgebra, 679 \item FpAlgebraOps.OperationQuotientModule, 1116 \item FpGroup \subitem for ag groups, 504 \item FpGroup for Ag Groups, 509 \item FpGroupPresentation, 467 \item FpGroupQClass, 651 \item Frame, 825 \item FrattiniSubgroup, 261 \subitem for character tables, 778 \item Free Modules, 692 \item FreeAlgebra, 678 \item FreeGroup, 460 \item Frobenius group, 637 \item Frobenius Schur indicator, 821 \item FrobeniusAutomorphism, 409 \item ftp, 901 \item function, 191 \item Function Calls, 184 \item Functions, 191 \item Functions depending on nauty, 1002 \item Functions for Character Tables, 778 \item Functions for Class Functions, 883 \item Functions for Finitely Presented Algebras, 680 \item Functions for Matrix Algebras, 686 \item Functions for MeatAxe Matrices, 1079 \item Functions for MeatAxe Matrix Algebras, 1082 \item Functions for MeatAxe Matrix Groups, 1081 \item Functions for MeatAxe Permutations, 1081 \item Functions for Quotient Spaces, 612 \item Functions for Row Modules, 696 \item Functions for Row Space Cosets, 611 \item Functions for Row Spaces, 605 \item Functions to construct and modify graphs, 980 \item Functions to construct new graphs from old, 994 \item Functions to determine regularity properties of graphs, 990 \item Functions to inspect graphs, vertices and edges, 985 \item Further Information, 976 \item fusion \subitem store, 808 \item fusion map \subitem get, 807 \item fusion of classes, 793 \item FusionCharTableTom, 764 \item FusionConjugacyClasses, 808 \subitem for character tables, 778 \item fusions, 851 \item FusionsAllowedByRestrictions, 858 \indexspace \item Galois, 396 \item galois automorphism, 369 \item galois conjugate \subitem unique, 371 \item galois conjugate characters, 372 \item Galois conjugates \subitem of a field element, 245 \item galois conjugation, 369 \item galois field, 403 \item Galois group \subitem of a field, 242 \subitem of an extension field, 393 \item GaloisCyc, 369 \item GaloisField, 408 \item GaloisGroup, 242 \subitem for finite fields, 410 \item GaloisGroup for Extension Fields, 393 \item GaloisGroup for Number Fields, 386 \item GaloisMat, 372 \item GaloisType, 396 \item GAP for MS-DOS, 914 \item GAP for TOS, 922 \item GAP for UNIX, 907 \item gap.rc, 920, 927 \item GAPChars, 809 \item GapObject, 1074 \item Gaussians, 375 \item Gcd, 234 \subitem for polynomials, 422, 423 \item GcdRepresentation, 235 \item GeneralizedSrivastavaCode, 1024 \item GeneralLinearGroup, 631 \item GeneralUnitaryGroup, 632 \item Generating Cyclic Codes, 1026 \item Generating Linear Codes, 1020 \item Generating Systems of Ag Groups, 520 \item Generating Unrestricted Codes, 1016 \item generator \subitem of the prime residue group, 357, 358 \item GeneratorMat, 1045 \item GeneratorMatCode, 1021 \item GeneratorPol, 1046 \item GeneratorPolCode, 1026 \item generators \subitem of Galois group, 385 \item GeneratorsPrimeResidues, 385 \item Generic Character Tables, 813 \item generic character tables, 780, 865 \item GeodesicsGraph, 998 \item GetFusionMap, 807 \item Getting and Installing GAP, 901 \item Getting Character Tables, 780 \item Getting GAP, 901 \item GF, 408 \item Girth, 989 \item GlobalParameters, 991 \item GModule, 1097 \item GoppaCode, 1023 \item Grape, 979 \item GRAPE Package, 946 \item Graph, 980 \item GrayMat, 1064 \item GreedyCode, 1019 \item Group, 254 \subitem for ag groups, 501 \item Group Constructions, 300 \item Group Elements, 250 \item Group for Ag Groups, 505 \item Group for MeatAxe Matrices, 1079 \item Group Functions for Ag Groups, 501 \item Group Functions for Finitely Presented Groups, 461 \item Group Functions for Matrix Groups, 626 \item Group Functions for Permutation Groups, 441 \item Group Homomorphisms, 304 \item group homomorphisms \subitem by images, 309 \subitem conjugation, 308 \subitem inner, 309 \subitem natural, 307 \subitem operation, 330 \item Group Libraries, 629 \item Group Records, 313 \item GroupHomomorphismByImages, 309 \item GroupHomomorphismsByImages \subitem for permutation groups, 446 \item GroupId, 276 \item Groups, 249 \item GUAVA, 1005 \indexspace \item HadamardCode, 1017 \item HadamardMat, 1065 \item HallConjugatingWordAgGroup, 541 \item HallSubgroup, 526 \item HammingCode, 1022 \item Hecke, 1140 \item HeckeCharTable, 1142 \item HeckeReflectionRepresentation, 1141 \item Help, 201 \item help \subitem abbreviating, 203 \subitem browsing, 202 \subitem format, 201 \subitem index, 203 \subitem redisplaying, 203 \subitem scrolling, 201 \item Help Index, 203 \item Hermann-Mauguin symbol, 650 \item HomGMod, 1101 \item Homomorphisms, 719 \item homomorphisms \subitem by images, group, 309 \subitem conjugation, group, 308 \subitem Frobenius, field, 409 \subitem inner, group, 309 \subitem natural, group, 307 \subitem of algebras, 673 \subitem of fields, 246 \subitem of groups, 304 \subitem operation, group, 330 \item Homomorphisms for Permutation Groups, 446 \item HorizontalConversionFieldMat, 1068 \item How to Extend a Table Library, 877 \item HP-UX, 907 \indexspace \item ideal decomposition, 396 \item IdempotentsTom, 765 \item Identical Lists, 559 \item Identical Records, 731 \item Identifiers, 182 \item IdentityMapping, 716 \item IdentityMat, 618 \item IdWord, 451 \item If, 188 \item if, 188 \item if statement, 188 \item Igs, 522 \item Image, 708 \subitem for blocks homomorphisms, 447 \subitem for field homomorphisms, 247 \subitem for Frobenius automorphisms, 409 \subitem for group homomorphisms, 307 \subitem for GroupHomomorphismByImages, 310 \subitem for GroupHomomorphismByImages for permutation groups, 446 \subitem for OperationHomomorphism, 330 \subitem for transitive constituent homomorphisms, 447 \item Images, 710 \subitem for field homomorphisms, 247 \subitem for group homomorphisms, 307 \item ImagesRepresentative, 711 \subitem for GroupHomomorphismByImages, 310 \item In, 563 \item in \subitem for ag groups, 499 \subitem for algebraic Elements, 392 \subitem for Conjugacy Classes, 281 \subitem for conjugacy classes of subgroups, 289 \subitem for domains, 216 \subitem for finite fields, 409 \subitem for finitely presented groups, 461 \subitem for gaussians, 377 \subitem for matrix groups, 625 \subitem for records, 736 \item In for Records, 736 \item IncludeIrreducibles, 785 \item IndependentSet, 994 \item Indeterminate, 413 \item Indeterminateness, 850 \item Index, 271 \subitem for finitely presented groups, 462 \item Indicator, 821 \item Indirected, 861 \item Induced, 828 \subitem for character tables, 778 \item InducedCyclic, 828 \item InducedGMod, 1098 \item InducedSubgraph, 994 \item Inequalities, 831 \item InertiaSubgroup, 887 \item Inflated, 827 \item InfoLattice1, 288 \item InitClassesCharTable, 796 \item InitFusion, 855 \item InitialiseSeed, 1104 \item initialize classlengths, 796 \item InitPowermap, 852 \item InitPQp, 516 \item InitSQ, 519 \item InnerAutomorphism, 309 \item InnerDistribution, 1049 \item installation, 901 \subitem under MS-DOS, 916 \subitem under TOS, 923 \subitem under UNIX, 908 \subitem under Windows, 916 \item Installation of GAP for MS-DOS, 916 \item Installation of GAP for TOS, 923 \item Installation of GAP for UNIX, 908 \item Installing the ANU pq Package, 935 \item Installing the ANU Sq Package, 943 \item Installing the GRAPE Package, 947 \item Installing the MeatAxe Package, 950 \item Installing the NQ Package, 952 \item Installing the SISYPHOS Package, 955 \item Installing the Smash Package, 957 \item Installing the Vector Enumeration Package, 958 \item Installing the Weyl Package, 960 \item Installing the XGap Package, 962 \item Int, 346 \item IntCyc, 367 \item integer part of a quotient, 345 \item Integers, 343 \item Integral Bases for Number Fields, 387 \item IntegralizedMat, 820 \item InterpolatedPolynomial, 419 \item IntersectBlist, 584 \item Intersection, 217 \subitem for ag groups, 500 \subitem for double cosets, 299 \subitem for finite fields, 409 \subitem for finitely presented groups, 461 \subitem for groups, 311 \subitem for matrix groups, 625 \subitem for Permutation Groups, 441 \subitem for right cosets, 294 \subitem of vector spaces, 339 \item intersection \subitem of boolean lists, 583, 584 \subitem of domains, 217 \subitem of sets, 578, 579 \item Intersection for Ag Groups, 500 \item Intersection for Groups, 312 \item Intersection for MeatAxe Modules, 1083 \item IntersectionBlist, 583 \item IntersectionCode, 1041 \item Intersections of Ag Groups, 533 \item IntersectionsTom, 763 \item IntersectionSumAgGroup, 534 \item IntersectSet, 578 \item IntFFE, 407 \item InverseClassesCharTable, 797 \item InverseMap, 846 \item InverseMapping, 716 \subitem for GroupHomomorphismByImages, 311 \item InverseMatMod, 820 \item Irr, 887 \item irrationalities, 365 \item IrreducibleDifferences, 826 \item IrreducibleSolvableGroup, 646 \item IsAbelian, 271 \subitem for character tables, 778 \item IsAbsIrredGMod, 1100 \item IsAbsolutelyIrreducible for MeatAxe Modules, 1083 \item IsAgGroup, 510 \item IsAgWord, 492 \item IsAlgebra, 665 \item IsAlgebraElement, 675 \item IsAlgebraicElement, 395 \item IsAlgebraicExtension, 392 \item IsAssociated, 228 \subitem for gaussians, 378 \item IsAutomorphism, 722 \item IsBijection, 704 \item IsBipartite, 989 \item IsBlist, 582 \item IsBool, 727 \item IsBound, 738 \item IsCentral, 271 \item IsCharacter, 886 \item IsCharTable, 777 \item IsClassFunction, 886 \item IsCode, 1014 \item IsCodeword, 1007 \item IsCommutativeRing, 226 \item IsCompatiblePCentralSeries, 1091 \item IsCompleteGraph, 990 \item IsConjugacyClass, 280 \item IsConjugacyClassSubgroups, 289 \item IsConjugate, 272 \item IsConnectedGraph, 989 \item IsConsistent, 510 \item IsCoset, 293 \item IsCyc, 367 \item IsCycInt, 367 \item IsCyclic, 272 \subitem for ag groups, 503 \subitem for character tables, 778 \item IsCyclic for Ag Groups, 506 \item IsCyclicCode, 1014 \item IsCyclicTom, 764 \item IsCyclotomicField, 382 \item IsDistanceRegular, 991 \item IsDoubleCoset, 298 \item IsEdge, 987 \item IsElementAgSeries, 529 \item IsElementaryAbelian, 272 \item IsElementaryAbelianAgSeries, 511 \item IsEndomorphism, 722 \item IsEpimorphism, 721 \item IsEqualSet, 576 \item IsEquivalent, 1052 \item IsEquivalent for MeatAxe Modules, 1083 \item IsEquivalent for Row Modules, 696 \item IsEquivalentOperation, 335 \item IsEuclideanRing, 227 \item IsFFE, 406 \item IsField, 239 \item IsFieldHomomorphism, 246 \item IsFinite, 216 \subitem for ag groups, 503 \subitem for double cosets, 298 \subitem for right cosets, 294 \subitem for vector spaces, 339 \item IsFixpoint, 322 \item IsFixpointFree, 322 \item IsFpAlgebra, 679 \item IsFpAlgebraElement, 681 \item IsFreeModule, 695 \item IsGaussInt, 377 \item IsGaussRat, 377 \item IsGeneralMapping, 702 \item IsGModule, 1097 \item IsGraph, 985 \item IsGroup, 255 \item IsGroupElement, 251 \item IsGroupHomomorphism, 305 \item IsHomomorphism, 719 \subitem for fields, 246 \subitem for groups, 305 \item IsIdentical, 560 \item IsIdenticalPresentationFpGroup, 465 \item IsInjective, 703 \subitem for field homomorphisms, 247 \subitem for group homomorphisms, 306 \item IsInStandardForm, 1067 \item IsInt, 346 \item IsIntegralRing, 226 \item IsIrredGMod, 1099 \item IsIrreducible, 230 \subitem for gaussians, 378 \item IsIrreducible for MeatAxe Modules, 1083 \item IsIrreducible for Row Modules, 697 \item IsIsomorphic, 1092 \item IsIsomorphicGraph, 1002 \item IsIsomorphicPGroup, 972 \item IsIsomorphism, 721 \item IsLatinSquare, 1068 \item IsLaurentPolynomialRing, 421 \item IsLeftCoset, 296 \item IsLinearCode, 1014 \item IsList, 554 \item IsLoopy, 986 \item IsMapping, 702 \subitem for GroupHomomorphismByImages, 310 \subitem for GroupHomomorphismByImages for permutation groups, 446 \item IsMat, 617 \item IsMatAlgebra, 686 \item IsMDSCode, 1050 \item IsMeatAxeMat, 1077 \item IsMeatAxePerm, 1080 \item IsMinimalNonmonomial, 899 \item IsModule, 694 \item IsMonomial for characters, 897 \item IsMonomial for groups, 897 \item IsMonomorphism, 720 \item IsNilpotent, 273 \subitem for ag group, 503 \subitem for character tables, 779 \item IsNormal, 273 \subitem for ag groups, 503 \item IsNormal for Ag Groups, 506 \item IsNormalExtension, 393 \item IsNormalized, 522 \item IsNullGraph, 990 \item IsNumberField, 382 \item isoclinic table, 791 \item IsomGMod, 1100 \item Isomorphisms, 1093 \item IsParent, 253 \item IsPerfect, 274 \subitem for ag group, 503 \item IsPerfectCode, 1050 \item IsPerm, 427 \item IsPermChar, 830 \item IsPermGroup, 431 \item IsPNilpotent, 529 \item IsPolynomial, 414 \item IsPolynomialRing, 420 \item IsPrime, 230 \subitem for gaussians, 378 \item IsPrimeInt, 350 \item IsPrimePowerInt, 351 \item IsPrimitive, 332 \item IsPrimitive for Characters, 895 \item IsPrimitiveGMod, 1104 \item IsPrimitiveRootMod, 357 \item IsQuasiPrimitive, 894 \item IsRange, 594 \item IsRat, 361 \item IsRec, 738 \item IsRegular, 325 \item IsRegularGraph, 991 \item IsRightCoset, 293 \item IsRing, 223 \item IsRowSpace, 606 \item IsSelfDualCode, 1051 \item IsSelfOrthogonalCode, 1051 \item IsSemiEchelonBasis, 609 \item IsSemiRegular, 326 \subitem for Permutation Groups, 445 \item IsSet, 576 \item IsSimple, 274 \subitem for character tables, 779 \item IsSimpleGraph, 987 \item IsSolvable, 274 \subitem for character tables, 779 \subitem for Permutation Groups, 443 \item IsSpaceCoset, 611 \item IsString, 591 \item IsSubalgebra, 666 \item IsSubgroup, 275 \subitem for ag groups, 503 \item IsSubgroup for Ag Groups, 506 \item IsSubnormal, 275 \item IsSubnormallyMonomial, 896 \item IsSubset, 217 \subitem for ag groups, 499 \subitem for groups, 311 \subitem for sets, 578 \item IsSubsetBlist, 583 \item IsSubspace, 339 \item IsSupersolvable \subitem for character tables, 779 \item IsSurjective, 703 \subitem for field homomorphisms, 247 \subitem for group homomorphisms, 306 \item IsTransitive, 323 \item IsTrivial \subitem for groups, 276 \item IsTrivial for Groups, 276 \item IsUniqueFactorizationRing, 227 \item IsUnit, 228 \subitem for gaussians, 378 \subitem for matrix rings, 624 \item IsUnitalAlgebra, 665 \item IsUnknown, 400 \item IsVector, 599 \item IsVectorSpace, 338 \item IsVertex, 985 \item IsVirtualCharacter, 886 \item IsWord, 454 \item iterate a function over a list, 572 \item Iterated, 572 \indexspace \item Jacobi, 358 \item JenningsSeries, 266 \item JohnsonGraph, 983 \indexspace \item KazhdanLusztigPolynomial, 1138 \item Kernel, 723 \subitem for blocks homomorphisms, 447 \subitem for fields, 247 \subitem for groups, 305 \subitem for OperationHomomorphism, 330 \item Kernel for class functions, 883 \item KernelChar, 820 \item KernelFieldHomomorphism, 247 \item KernelGroupHomomorphism, 305 \item Keywords, 182 \item KLCoefficient, 1138 \item Krawtchouk, 1069 \item KrawtchoukMat, 1064 \item Kronecker product, 788 \item KroneckerProduct, 619 \item KroneckerProduct for MeatAxe matrices, 1079 \item KroneckerProduct for MeatAxe Modules, 1083 \indexspace \item Lambda, 356 \item larger prime, 351 \item LargestMovedPointPerm, 427 \item LargestPrimeOrderElement, 1105 \item LargestPrimePowerOrderElement, 1106 \item last, 197 \item Lattice, 283 \item lattice base reduction, 834--836 \item Lattice for MeatAxe Modules, 1083 \item LaurentPolynomialRing, 420 \item Layers, 993 \item Lcm, 235 \item LeadingCoefficient, 418 \item LeadingExponent, 492 \item LeftCellRepresentation, 1140 \item LeftCells, 1139 \item LeftCoset, 296 \item LeftCosets, 295 \item LeftNormedComm \subitem for group elements, 251 \item LeftQuotient \subitem for group elements, 251 \subitem for words, 453 \item Legendre, 358 \item Length, 556 \item length \subitem of a list, 556 \subitem of a string, 591 \subitem of a word, 455 \item LengthenedCode, 1037 \item LengthString, 591 \item LengthWord, 455 \item LenstraBase, 387 \item Lexical Structure, 180 \item LexiCode, 1020 \item libraries of character tables, 865 \item library of character tables, 868, 871, 875 \item library tables, 780, 865 \subitem add, 877 \subitem generic, 813 \item Line Editing, 199 \item LinearCombination, 341 \subitem in vector space, 341 \item LinearIndependentColumns, 819 \item LinearOperation, 532 \item List, 554 \item list \subitem of primes, 350 \item List Assignment, 556 \item List Elements, 555 \item ListBlist, 582 \item ListPerm, 428 \item Lists, 553 \item lists \subitem boolean, 581 \item ListStabChain, 438 \item LLL, 836 \item LLL algorithm \subitem for characters, 836 \subitem for Gram matrices, 835 \subitem for vectors, 834 \item LLLReducedBasis, 834 \item LLLReducedGramMat, 835 \item load \subitem a file, 204 \subitem a library file, 205 \item local, 191 \item LocalParameters, 991 \item log \subitem to a file, 206 \item log input \subitem to a file, 206 \item logarithm \subitem of a finite field element, discrete, 408 \item logarithm of an integer, 347 \item LogFFE, 408 \item logical, 725 \item logical operations, 726 \item LogInputTo, 206 \item LogInt, 347 \item LogTo, 206 \item LongestWeylWord, 1135 \item loop \subitem for, 190 \subitem read eval print, 197 \subitem repeat, 189 \subitem while, 189 \item LowerBoundMinimumDistance, 1062 \item LowerCentralSeries, 267 \subitem for ag groups, 502 \subitem for character tables, 779 \item LowIndexSubgroupsFpGroup, 466 \item Lucas, 754 \indexspace \item Main Loop, 197 \item MAKElb11, 809 \item MakeStabChain, 435 \item MakeStabChainStrongGenerators, 436 \item Manipulating Codes, 1031 \item map, 554 \subitem composition, 846 \subitem indeterminateness, 850 \subitem indirection by a, 861 \subitem inverse of a, 846 \subitem parametrize, 847 \subitem parametrized, 845 \item MappedExpression, 681 \item MappedWord, 457 \item Mapping Functions for Algebra Homomorphisms, 673 \item Mapping Functions for Field Homomorphisms, 247 \item Mapping Functions for Group Homomorphisms, 306 \item Mapping Records, 717 \item MappingByFunction, 717 \item MappingPermListList, 429 \item Mappings, 701 \item maps, 845 \item Maps and Parametrized Maps, 845 \item Marks, 760 \item MatAlgebra, 687 \item MatAutomorphisms, 805 \item MatClassMultCoeffsCharTable, 798 \item MatGroupAgGroup, 511 \item MatGroupSagGroup, 550 \item MatGroupZClass, 654 \item MatRepresentationsPGroup, 795 \item Matrices, 615 \item Matrices for Codes, 1063 \item matrix, 615 \item Matrix Algebras, 685 \item matrix automorphisms, 860, 861 \item Matrix Group Records, 627 \item Matrix Groups, 625 \item Matrix Representations of Finite Polycyclic Groups, 795 \item Matrix Rings, 623 \item MatrixOrder, 1106 \item MatScalarProducts, 818 \item MatTom, 761 \item MaximalElement, 531 \item MaximalNormalSubgroups \subitem for character tables, 779 \item MaximalSubgroups, 291 \item Maximum, 571 \item maximum \subitem of a list, 571 \subitem of integers, 571 \item MeatAxe Matrices, 1077 \item MeatAxe Matrix Algebras, 1082 \item MeatAxe Matrix Groups, 1081 \item MeatAxe Modules, 1083 \item MeatAxe Object Records, 1085 \item MeatAxe Package, 950 \item MeatAxe Permutations, 1080 \item MeatAxe.Unbind, 1085 \item MeatAxeMat, 1077 \item MeatAxePerm, 1080 \item membership test \subitem for ag groups, 499 \subitem for algebraic extensions, 392 \subitem for domains, 216 \subitem for finite fields, 409 \subitem for gaussians, 377 \subitem for records, 736 \item Membership Test for Domains, 216 \item membershiptest \subitem for groups, 312 \item MergedCgs, 522 \item MergedIgs, 523 \item mersenne primes, 353 \item MinBlocks, 1104 \item minimal polynom \subitem of a field element, 243 \item MinimalGeneratingSet, 529 \item MinimalNonmonomialGroup, 899 \item Minimum, 572 \item minimum \subitem of a list, 572 \subitem of integers, 572 \item MinimumDistance, 1047 \item MinPol, 243 \item MinpolFactors, 393 \item MinSubGMods, 1101 \item MinusCharacter, 825 \item Miscellaneous functions, 1069 \item MOC \subitem interface to, 809, 811 \item MOCChars, 809 \item MOCTable, 809 \item Mod, 233 \item mod for character tables, 779 \item Modified Todd-Coxeter, 471 \item modular roots, 359 \item Module, 693 \item Module for MeatAxe Matrix Algebras, 1082 \item Module Functions for MeatAxe Modules, 1083 \item Module Homomorphism Records, 699 \item Module Homomorphisms, 697 \item Modules, 691 \item ModulesSQ, 519 \item Moebius inversion function, 354 \item MoebiusMu, 354 \item MoebiusTom, 764 \item MolienSeries, 822 \item MOLS, 1065 \item MOLSCode, 1018 \item Monomial Representations of Finite Polycyclic Groups, 795 \item Monomiality Questions, 891 \item More about Ag Groups, 497 \item More about Ag Words, 489 \item More about Algebras, 662 \item More about Boolean Lists, 585 \item More about Class Functions, 881 \item More about Cyclotomics, 365 \item More about Dispatchers, 211 \item More about Finitely Presented Algebras, 677 \item More about Generic Character Tables, 813 \item More about Groups and Subgroups, 252 \item More about Maps and Parametrized Maps, 845 \item More about Matrix Algebras, 685 \item More about Modules, 691 \item More about Monomiality Questions, 891 \item More about Ranges, 594 \item More about Row Spaces, 601 \item More about Sets, 579 \item More about Special Ag Groups, 545 \item More about Tables of Marks, 757 \item More about the MeatAxe in GAP, 1074 \item More about Vector Enumeration, 1116 \item More about Vectors, 599 \item MS-DOS \subitem features, 920 \subitem installation, 916 \subitem options, 920 \item MSDOS, 914 \item multiplicative order of an integer, 357 \item multiply \subitem the elements of a list, 571 \item multisets, 575 \item Multivariate Polynomials, 413 \item Murnaghan components, 825, 826 \indexspace \item NaturalHomomorphism, 307 \item NaturalModule, 689 \item NaturalModule for MeatAxe Matrix Algebras, 1082 \item NewGroupGraph, 1000 \item newline, 181 \item NextClassPQp, 516 \item NextModuleSQ, 520 \item NextPrimeInt, 351 \item NF, 382 \item NilpotentQuotient, 952 \item NK, 370 \item NofCyc, 368 \item NoMessageScalarProduct \subitem for character tables, 779 \item NonsplitExtension, 975 \item NordstromRobinsonCode, 1019 \item Norm, 244 \subitem for algebraic extensions, 394 \subitem for finite fields, 410 \subitem for gaussians, 378 \item norm \subitem of a field element, 244 \item Norm for class functions, 883 \item normal subgroup \subitem table of, 788 \item NormalBaseNumberField, 388 \item NormalClosure, 261 \subitem for character tables, 779 \item NormalIntersection, 261 \subitem for ag groups, 502 \item Normalize, 522 \item Normalized, 522 \item NormalizedAutomorphisms, 1091 \item NormalizedOuterAutomorphisms, 1091 \item NormalizedUnitsGroupRing, 1094 \item Normalizer, 261 \subitem for ag groups, 502 \subitem for finitely presented groups, 462 \subitem for matrix groups, 626 \subitem for Permutation Groups, 441 \item Normalizer for Ag Groups, 505 \item NormalizerTom, 763 \item NormalizerZClass, 654 \item NormalSubgroupClasses, 889 \item NormalSubgroups, 291 \subitem for character tables, 779 \item NormedVector, 599 \item NormedVectors, 607 \item not, 726 \item NotifyCharTable, 877 \item NQ Package, 952 \item NrCombinations, 746 \item NrCrystalFamilies, 648 \item NrCrystalSystems, 649 \item NrDadeGroups, 656 \item NrDerangements, 749 \item NrOrderedPartitions, 751 \item NrPartitions, 750 \item NrPartitionsSet, 750 \item NrPermutationsList, 748 \item NrPolyhedralSubgroups, 799 \item NrQClassesCrystalSystem, 649 \item NrRestrictedPartitions, 752 \item NrSpaceGroupTypesZClass, 656 \item NrSubs, 760 \item NrTuples, 748 \item NrUnorderedTuples, 747 \item NrZClassesQClass, 653 \item NullAlgebra, 688 \item NullCode, 1030 \item NullGraph, 982 \item NullMat, 618 \item NullspaceMat, 621 \item NullWord, 1010 \item Number, 567 \item number \subitem Bell, 744 \subitem binomial, 744 \subitem of divisors of an integer, 353 \subitem of elements in a list, 567 \subitem Stirling, of the first kind, 745 \subitem Stirling, of the second kind, 745 \item Number Field Records, 382 \item number fields \subitem Galois group, 386 \item Number Theory, 355 \item NumberAlgebraElement, 683 \item NumberConjugacyClasses, 529 \item NumberVector, 610 \item Numerator, 362 \item numerator \subitem of a rational, 362 \indexspace \item od, 190 \item Omega for characters, 883 \item One Cohomology Group, 536 \item OneCoboundaries, 536 \item OneCocycles, 537 \item OneIrreducibleSolvableGroup, 645 \item OnePrimitiveGroup, 636 \item OneSolvableGroup, 640 \item OneThreeGroup, 643 \item OneTwoGroup, 641 \item OnLeft, 318 \item OnLeftCosets, 318 \item OnLines, 318 \item OnPairs, 318 \item OnPoints, 318 \item OnRight, 318 \item OnRightCosets, 318 \item OnSets, 318 \item OnTuples, 318 \item Operation, 329 \item Operation for Algebras, 672 \item Operation for Finitely Presented Algebras, 1115 \item Operation for MeatAxe Matrix Groups, 1081 \item OperationCosetsFpGroup, 465 \item OperationHomomorphism, 330 \subitem for blocks, 447 \subitem for transitive constituents, 446 \item OperationHomomorphism for Algebras, 673 \item OperationHomomorphism for Modules, 697 \item OperationModule, 697 \item Operations, 186 \item operations \subitem for booleans, 726 \subitem for groups, 312 \subitem for integers, 344 \subitem for lists, 562 \subitem for polynomials, 415 \subitem for rationals, 363 \subitem for vectors, 598 \item Operations for algebraic elements, 392 \item Operations for Algebras, 668 \item Operations for Booleans, 726 \item Operations for Codes, 1015 \item Operations for Codewords, 1008 \item Operations for Cyclotomics, 369 \item Operations for Field Elements, 242 \item Operations for Finite Field Elements, 405 \item Operations for Gaussians, 376 \item Operations for Group Elements, 250 \item Operations for Groups, 312 \item Operations for Integers, 344 \item Operations for Lists, 562 \item Operations for Mappings, 706 \item Operations for Matrices, 615 \item Operations for MeatAxe Matrices, 1078 \item Operations for MeatAxe Permutations, 1081 \item Operations for Permutations, 426 \item Operations for Polynomials, 415 \item Operations for Quotient Spaces, 612 \item Operations for Rationals, 363 \item Operations for Records, 735 \item Operations for Ring Elements, 225 \item Operations for Row Modules, 695 \item Operations for Row Space Cosets, 610 \item Operations for Row Spaces, 604 \item Operations for Unknowns, 401 \item Operations for Vectors, 598 \item Operations for Words, 453 \item Operations of Groups, 317 \item Operations of Permutation Groups, 445 \item operations record, 210 \item Operations Records for Character Tables, 778 \item operators \subitem for cyclotomics, 368, 369 \item Operators for Character Tables, 779 \item Operators for Class Functions, 882 \item Operators for Finitely Presented Algebras, 680 \item OptimalityCode, 1061 \item OptimalityLinearCode, 1062 \item options, 901 \subitem under MS-DOS, 920 \subitem under TOS, 927 \subitem under UNIX, 912 \item or, 726 \item Orbit, 326 \subitem for ag groups, 503 \item Orbitalgorithms of Ag Groups, 531 \item OrbitalGraphIntersectionMatrices, 992 \item OrbitFusions, 859 \item OrbitLength, 327 \item OrbitLengths, 329 \item OrbitPowermaps, 860 \item Orbits, 328 \item OrbitsCharacters, 887 \item Order, 252 \subitem for finitely presented groups, 462 \item order \subitem of a finite field element, 407 \subitem of a group element, 252 \subitem of the prime residue group, 356 \item Order for MeatAxe matrices, 1079 \item Order for MeatAxe Permutations, 1081 \item OrderedPartitions, 751 \item OrderFFE, 407 \item OrderGraph, 985 \item ordering \subitem of ag words, 490 \subitem of algebra elements, 674 \subitem of gaussians, 375 \subitem of group elements, 250 \subitem of group homomorphisms, 306 \subitem of records, 733 \item OrderMat, 620 \item OrderMod, 357 \item Organization of the Table Libraries, 875 \item OrthogonalComponents, 825 \item OrthogonalEmbeddings, 836 \item OrthogonalEmbeddingsSpecialDimension, 837 \item Other matrix functions, 1106 \item Other Operations, 318 \item OuterAutomorphisms, 1091 \item OuterDistribution, 1049 \item output \subitem suppressing, 197 \indexspace \item p-regular table, 791 \item PadicCoefficients, 820 \item paramap, 845 \item ParametersCentralizers, 1137 \item Parametrized, 847 \item parametrized maps, 845 \item Parent, 253 \item Parent Algebras and Subalgebras, 663 \item Parity check, 1032 \item part \subitem of a string, 590 \item Partitions, 750 \item partitions, 743 \subitem improper, of an integer, 751 \subitem of a set, 750 \subitem of an integer, 750 \subitem ordered, of an integer, 751 \subitem restricted, of an integer, 752 \item PartitionsSet, 750 \item PartitionTuples, 753 \item PCentralSeries, 267 \item PCore, 262 \item Permanent, 749 \item PermBounds, 832 \item PermCharInfo, 830 \item PermChars, 832 \item PermCharsTom, 764 \item PermGMod, 1098 \item PermGroup \subitem for matrix groups, 626 \item PermGroupAgGroup, 512 \item PermGroupOps.ElementProperty, 438 \item PermGroupOps.Indices, 437 \item PermGroupOps.LargestMovedPoint, 432 \item PermGroupOps.MovedPoints, 432 \item PermGroupOps.NrMovedPoints, 432 \item PermGroupOps.PgGroup, 440 \item PermGroupOps.SmallestMovedPoint, 432 \item PermGroupOps.StrongGenerators, 437 \item PermGroupOps.SubgroupProperty, 439 \item PermList, 429 \item PermRep, 976 \item PermRepresentationRoots, 1132 \item Permutation, 321 \item permutation character, 855 \item Permutation Character Candidates, 830 \item permutation characters, 832 \subitem candidates for, 830 \subitem faithful candidates for, 833 \item Permutation Group Records, 449 \item Permutation Groups, 431 \item PermutationCharacter, 279, 442 \item Permutations, 425 \item permutations \subitem fixpointfree, 749 \subitem list, 748 \item PermutationsList, 748 \item Permuted, 570 \item PermutedCode, 1033 \item PermutedCols, 1067 \item PermWeylWord, 1134 \item Phi, 356 \item PointGraph, 996 \item PolyCodeword, 1009 \item PolyhedralGroup, 631 \item Polynomial, 414 \item PolynomialRing, 420 \item Polynomials, 411 \item Porting GAP, 930 \item Position, 563 \item PositionProperty, 565 \item PositionSorted, 564 \item PositionWord, 456 \item Power, 829 \item power \subitem of algebra elements, 674 \subitem of gaussians, 376 \subitem of group elements, 250 \subitem of records, 735 \subitem of words, 453 \item Powermap, 851 \item PowerMapping, 715 \item powermaps, 851--854, 857, 860, 861 \item PowermapsAllowedBySymmetrisations, 857 \item PowerMod, 234 \item PowerPartition, 753 \item powerset, 746 \item Powmap, 862 \item Pq, 965 \item PqDescendants, 966 \item PqHomomorphism, 966 \item PqList, 969 \item PQp, 516 \item PQuotient, 513 \item precedence, 186 \item PrefrattiniSubgroup, 262 \item PreImage, 711 \subitem for blocks homomorphisms, 447 \subitem for field homomorphisms, 247 \subitem for group homomorphisms, 307 \subitem for OperationHomomorphism, 330 \item PreImages, 713 \subitem for field homomorphisms, 247 \subitem for group homomorphisms, 307 \subitem for transitive constituent homomorphisms, 447 \item PreImagesRepresentative, 714 \item Presentation Records, 466 \item PresentationFpGroup, 466 \item PresentationNormalClosure, 473 \item PresentationNormalClosureRrs, 473 \item PresentationSubgroup, 473 \item PresentationSubgroupMtc, 471 \item PresentationSubgroupRrs, 470 \item previous result, 197 \item PrevPrimeInt, 352 \item primary subgroup generators, 471, 472, 485 \item prime residue group, 355 \subitem exponent, 356 \subitem generator, 357, 358 \subitem order, 356 \item PrimeBlocks, 820 \item PrimeResidues, 355 \item Primes, 350 \item primes \subitem mersenne, 353 \item primitive element, 392 \item primitive root modulo an integer, 358 \item PrimitiveGroup, 636 \item PrimitiveRootMod, 358 \item PrimitiveUnityRoot, 1069 \item Print, 205 \subitem for character tables, 779 \subitem for double cosets, 299 \subitem for right cosets, 294 \item print \subitem to a file, 205 \item PrintAmbiguity, 850 \item PrintArray, 622 \item PrintCharTable, 777 \item PrintClassSubgroupLattice, 287, 288 \item PrintDefinitionFpAlgebra, 681 \item Printing and Saving Codes, 1044 \item Printing of Records, 737 \item PrintSisyphosInputPGroup, 1090 \item PrintSISYPHOSWord, 1089 \item PrintTo, 205 \item PrintToCAS, 811 \item PrintToLib, 877 \item PrintToMOC, 811 \item ProbabilityShapes, 396 \item Procedure Calls, 188 \item Product, 571 \item product \subitem for double cosets, 299 \subitem for right cosets, 295 \subitem of a group and a group element, 312 \subitem of algebra elements, 674 \subitem of gaussians, 376 \subitem of group elements, 250 \subitem of list and algebra element, 674 \subitem of list and group element, 251, 453 \subitem of records, 735 \subitem of words, 453 \item Profile, 207 \item Projection \subitem for subdirect products, 303 \subitem onto component of direct products, 300 \subitem onto component of semidirect products, 301 \item ProjectionMap, 847 \item prompt, 197 \subitem partial, 197 \item Properties and Property Tests, 268 \item Property Tests for Algebras, 670 \item PRump, 526 \item PuncturedCode, 1032 \item PutStandardForm, 1066 \indexspace \item QRCode, 1029 \item Quadratic, 371 \item quadratic irrationalities, 371 \item quadratic number fields, 371 \item quadratic residue, 358, 359 \item QuoInt, 345 \item Quotient, 226 \item quotient \subitem of gaussians, 376 \subitem of group elements, 250 \subitem of groups, 313 \subitem of list and group element, 251 \subitem of list and word, 453 \subitem of records, 735 \subitem of words, 453 \item Quotient Space Records, 614 \item Quotient Spaces, 603 \item QuotientGraph, 997 \item QuotientMod, 233 \item QuotientRemainder, 232 \subitem for gaussians, 378 \subitem for polynomials, 421 \indexspace \item Radical, 263 \item Random, 220 \subitem Methods for Permutation Groups, 448 \subitem for ag groups, 503 \subitem for algebraic Extensions, 392 \subitem for Conjugacy Classes, 281 \subitem for double cosets, 299 \subitem for finite fields, 409 \subitem for gaussians, 377 \subitem for matrix groups, 625 \subitem for Permutation Groups, 440 \subitem for right cosets, 294 \item random element \subitem of a domain, 220 \item Random Methods for Permutation Groups, 448 \item RandomCode, 1019 \item RandomElement, 1105 \item RandomLinearCode, 1025 \item RandomList, 572 \item RandomOrders for MeatAxe Matrix Algebras, 1082 \item RandomOrders for MeatAxe Matrix Groups, 1081 \item RandomSeed, 573 \item Ranges, 593 \item Rank for MeatAxe matrices, 1079 \item RankMat, 620 \item rational characters, 373 \item RationalizedMat, 373 \item Rationals, 361 \item Read, 204 \item read \subitem a file, 204 \subitem a library file, 205 \item read eval print loop, 197 \item Reading Sections, 201 \item ReadLib, 205 \item RealClassesCharTable, 799 \item RecFields, 741 \item ReciprocalPolynomial, 1070 \item record \subitem operations, 210 \item Record Assignment, 730 \item record fields \subitem for algebraic extension fields, 395 \subitem for extension elements, 395 \item Records, 729 \item recursion, 191 \item recursive functions, 191 \item Redisplaying a Section, 203 \item Reduced, 822 \item Reduced Reidemeister-Schreier, 470 \item ReducedAgWord, 494 \item ReducedOrdinary, 823 \item ReducedWeylWord, 1135 \item ReduceStabChain, 436 \item Redundancy, 1047 \item ReedMullerCode, 1022 \item ReedSolomonCode, 1029 \item RefinedAgSeries, 512 \item RefinedSubnormalSeries, 526 \item regular classes, 791 \item RelativeOrder, 492 \item remainder of a quotient, 345 \item RemInt, 345 \item remove \subitem an element from a set, 577 \item RemovedElementsCode, 1035 \item RemoveEdgeOrbit, 984 \item RemoveRelator, 470 \item RemoveSet, 577 \item Repeat, 189 \item repeat, 189 \item repeat loop, 189 \item RepetitionCode, 1031 \item representation \subitem as a sum of two squares, 379 \item Representative, 220 \item representative \subitem of a domain, 220 \item RepresentativeOperation, 333 \subitem for matrix groups, 626 \subitem for Permutation Groups, 445 \item RepresentativeOperation for Matrix Algebras, 687 \item RepresentativesFusions, 860 \item RepresentativesOperation, 334 \item RepresentativesPowermaps, 861 \item RequirePackage, 934 \item residue \subitem quadratic, 358, 359 \item ResidueCode, 1037 \item Restricted, 827 \subitem for character tables, 779 \item Restricted Special Ag Groups, 547 \item RestrictedPartitions, 752 \item RestrictedPerm, 429 \item Return, 193 \item return, 193 \item reverse the elements of a list, 566 \item Reversed, 566 \item Right Cosets Records, 295 \item RightCoset, 293 \subitem for ag groups, 504 \item RightCoset for Ag Groups, 508 \item RightCosetGroupOps, 294 \item RightCosets, 292 \item RightNormedComm \subitem for group elements, 251 \item Ring, 224 \item ring \subitem for cyclotomic integers, 385 \item Ring Functions for Gaussian Integers, 378 \item Ring Functions for Integers, 349 \item Ring Functions for Laurent Polynomial Rings, 423 \item Ring Functions for Matrix Rings, 624 \item Ring Functions for Polynomial Rings, 421 \item Ring Records, 236 \item Rings, 223 \item root \subitem of 1 modulo an integer, 359 \subitem of an integer, 347 \subitem of an integer modulo another, 359 \subitem of an integer, smallest, 348 \item RootInt, 347 \item RootMod, 359 \item RootOf, 392 \item roots of unity, 365 \item RootsCode, 1028 \item RootsOfCode, 1046 \item RootsUnityMod, 359 \item Rootsystem, 1132 \item RoundCyc, 367 \item Row Module Records, 698 \item Row Modules, 692 \item Row Space Bases, 602 \item Row Space Basis Records, 613 \item Row Space Coset Records, 613 \item Row Space Cosets, 602 \item Row Space Records, 612 \item Row Spaces, 601 \item RowSpace, 604 \item Runtime, 206 \indexspace \item Save, 515 \subitem for presentation records, 469 \item SavePqList, 970 \item ScalarProduct, 817 \subitem for character tables, 779 \item scalars, 597 \item ScanMOC, 809 \item Schreier-Sims \subitem Random, 448 \item SchurMultiplier, 974 \item scope, 183 \item secondary subgroup generators, 471, 472, 485 \item SecondCohomologyDimension, 974 \item Selecting Library Tables, 867 \item Selection Functions, 632 \item selections, 743 \item SemidirectProduct, 301 \subitem for groups, 302 \item SemidirectProduct for Groups, 302 \item SemiEchelonBasis, 609 \item SemiLinearDecomp, 1102 \item sequence \subitem bernoulli, 755 \subitem fibonacci, 754 \subitem lucas, 754 \item Series of Subgroups, 265 \item Set, 576 \item set difference \subitem of domains, 219 \item Set Functions for Ag Groups, 499 \item Set functions for Algebraic Extensions, 392 \item Set Functions for Conjugacy Classes, 281 \item Set Functions for Double Cosets, 298 \item Set Functions for Finite Fields, 409 \item Set Functions for Finitely Presented Groups, 460 \item Set Functions for Gaussians, 377 \item Set Functions for Groups, 311 \item Set Functions for Integers, 348 \item Set Functions for Matrix Groups, 625 \item Set Functions for Matrix Rings, 623 \item Set Functions for Permutation Groups, 440 \item Set Functions for Rationals, 364 \item Set Functions for Right Cosets, 294 \item Set Functions for Sets, 578 \item Set Functions for Subgroup Conjugacy Classes, 289 \item Set Functions for Vector Spaces, 339 \item Set Theoretic Functions for Algebras, 669 \item Set Theoretic Functions for MeatAxe Modules, 1083 \item SetPrintLevel, 285, 288 \item Sets, 575 \item ShallowCopy, 740 \item Share Libraries, 933 \item short vectors spanning a lattice, 834, 836 \item ShortenedCode, 1036 \item ShortestVectors, 838 \item SiftedAgWord, 494 \item SiftedVector, 607 \item Sigma, 353 \item sign \subitem of an integer, 346 \item SignInt, 346 \item SignPartition, 753 \item SignPerm, 428 \item SimpleReflectionMatrices, 1132 \item SimplifiedFpGroup, 474 \item SimplifyPresentation, 475 \item Sisyphos, 1089 \item SISYPHOS Package, 954 \item Size, 217 \subitem for ag groups, 500 \subitem for character tables, 779 \subitem for Conjugacy Classes, 281 \subitem for conjugacy classes of subgroups, 290 \subitem for double cosets, 298 \subitem for finitely presented groups, 461 \subitem for matrix groups, 625 \subitem for Permutation Groups, 441 \subitem for right cosets, 294 \subitem of vector spaces, 339 \item size \subitem of a domain, 217 \item Size for Ag Groups, 500 \item Size for MeatAxe Modules, 1083 \item SizeBlist, 582 \item SizesConjugacyClasses \subitem for character tables, 779 \item SizeScreen, 206 \item smaller prime, 352 \item SmallestGeneratorPerm, 428 \item SmallestMovedPointPerm, 428 \item SmallestRootInt, 348 \item Smash Package, 957 \item Smash, Matrix Groups and $G$-Modules, 1097 \item SmashGMod, 1101 \item SolutionMat, 621 \item SolvableGroup, 640 \item SolvableQuotient, 517 \item Some Notes on Character Theory in GAP, 769 \item Some special vertex subsets of a graph, 992 \item Sort, 569 \item sort a list, 569 \item SortCharactersCharTable, 801 \item SortCharTable, 804 \item SortClassesCharTable, 803 \item Sortex, 570 \item SortParallel, 570 \item space, 181 \item SpaceGroup, 658 \item Special Ag Group Records, 548 \item Special Ag Groups, 545 \item special character sequences, 587 \item SpecialLinearGroup, 632 \item SpecialUnitaryGroup, 632 \item SphereContent, 1069 \item SpinBasis, 1100 \item split classes, 792 \item SplitCharacters, 785 \item SplitExtension, 975 \item SplittingField for MeatAxe Modules, 1083 \item Sq, 942 \item square root \subitem of an integer, 347 \item SrivastavaCode, 1024 \item StabChain, 434 \item StabChainOptions, 448 \item Stabilizer, 332 \subitem for ag groups, 504 \subitem for matrix groups, 626 \subitem for Permutation Groups, 445 \item Stabilizer Chains, 433 \item Stabilizer for Ag Groups, 506 \item StandardArray, 1054 \item StandardAssociate, 229 \subitem for gaussians, 378 \subitem for polynomials, 423, 424 \item StandardBasis for Row Modules, 696 \item StandardFormCode, 1039 \item StandardPresentation, 970 \item StarCyc, 371 \item Statements, 186 \item Stirling number of the first kind, 745 \item Stirling number of the second kind, 745 \item Stirling1, 745 \item Stirling2, 745 \item StoreFusion, 808 \item Storing Subgroup Information, 888 \item String, 589 \item Strings and Characters, 587 \item structure constant, 797, 798 \item Subalgebra, 665 \item SubdirectProduct, 302 \item Subfields of Cyclotomic Fields, 381 \item Subgroup, 255 \item subgroup and permutation character, 830 \item Subgroup Conjugacy Class Records, 290 \item subgroup fusions, 807, 808, 851, 855--860 \item subgroup generators tree, 485 \item Subgroup Presentations, 470 \item SubgroupFusions, 851 \item Subgroups, 256 \item subgroups \subitem polyhedral, 799 \item Subgroups and Properties of Ag Groups, 525 \item Sublist, 566 \item Submodule, 693 \item SubnormalSeries, 267 \item SubQuotGMod, 1099 \item Subroutines of Decomposition, 819 \item subset test \subitem for domains, 217 \item subsets, 581, 746 \item Subspace, 606 \item Subspaces and Parent Spaces, 603 \item SubstitutedWord, 456 \item SubString, 590 \item substring \subitem of a string, 590 \item subtract \subitem a boolean list from another, 584 \subitem a set from another, 578 \item SubtractBlist, 584 \item SubtractSet, 578 \item Subword, 455 \item Sum, 571 \item sum \subitem of algebra elements, 674 \subitem of divisors of an integer, 353 \subitem of gaussians, 376 \subitem of list and algebra element, 674 \subitem of records, 735 \item SumAgGroup, 535 \item SumAgWord, 494 \item SumFactorizationFunctionAgGroup, 535 \item SumIntersectionSpaces for MeatAxe matrices, 1079 \item SunOS, 907 \item SupersolvableResiduum \subitem for character tables, 779 \item Support, 1011 \item SylowComplements, 527 \item SylowSubgroup, 263 \subitem for ag groups, 502 \subitem for matrix groups, 626 \subitem for Permutation Groups, 441 \item SylowSystem, 527 \item SylvesterMat, 1064 \item Symbols, 180 \item symmetric group \subitem powermap, 753 \item SymmetricGroup, 631 \item SymmetricParts, 824 \item Symmetrisations, 824 \item symmetrizations \subitem orthogonal, 825 \subitem symplectic, 826 \item SymplecticComponents, 826 \item SymplecticGroup, 632 \item SymTensorProductDecomp, 1103 \item Syndrome, 1053 \item SyndromeTable, 1054 \item syntax errors, 197 \item System V, 907 \item SystemNormalizer, 528 \item SysV, 907 \indexspace \item table automorphisms, 857, 859, 860 \item table of factor group, 787 \item Table of Marks Records, 758 \item table of normal subgroup, 788 \item TableAutomorphisms, 806 \item TableOfMarks, 759 \item tables, 769, 780, 865 \subitem add to a library, 877 \subitem format, 771, 775 \subitem generic, 813, 814, 816 \subitem libraries of, 865 \subitem library, 868, 871, 875 \subitem sort, 801, 803, 804 \item Tables of Marks, 757 \item tabulator, 181 \item Tau, 353 \item tensor product, 788 \item Tensored, 823 \item TensorProductDecomp, 1102 \item TensorProductGMod, 1098 \item TernaryGolayCode, 1027 \item test \subitem for a boolean, 727 \subitem for a cyclotomic, 367 \subitem for a cyclotomic field, 382 \subitem for a cyclotomic integer, 367 \subitem for a finite field element, 406 \subitem for a list, 554 \subitem for a power of a prime, 351 \subitem for a prime, 350 \subitem for a primitive root, 357 \subitem for a range, 594 \subitem for a rational, 361 \subitem for a set, 576 \subitem for a string, 591 \subitem for a vector, 599 \subitem for algebra element, 674 \subitem for algebraic element, 395 \subitem for algebraic extension, 392 \subitem for an integer, 346 \subitem for gaussian integer, 377 \subitem for gaussian rational, 377 \subitem for group element, 251 \subitem for list elements, 738 \subitem for membership, 563 \subitem for normal extension, 393 \subitem for number field, 382 \subitem for record elements, 738 \subitem for records, 738 \subitem for set equality, 576 \subitem for subsets, 578 \item TestCharTable, 777 \item TestConsistencyMaps, 856 \item TestHomogeneous, 893 \item TestInducedFromNormalSubgroup, 895 \item TestMonomial, 897 \item TestMonomialQuick, 897 \item TestQuasiPrimitive, 894 \item TestRelativelySM, 898 \item TestSubnormallyMonomial, 896 \item TestTom, 762 \item The 2-Groups Library, 641 \item The 3-Groups Library, 643 \item The Basic Groups Library, 629 \item The Crystallographic Groups Library, 647 \item The Irreducible Solvable Linear Groups Library, 645 \item The Library of Tables of Marks, 758 \item The MeatAxe, 1073 \item The Prime Quotient Algorithm, 513 \item The Primitive Groups Library, 636 \item The Programming Language, 179 \item The Solvable Groups Library, 640 \item The Solvable Quotient Algorithm, 517 \item The Syntax in BNF, 193 \item The Transitive Groups Library, 638 \item The XGap Package, 962 \item then, 188 \item ThreeGroup, 643 \item Tietze options, 482 \item Tietze record, 466 \item Tietze Transformations, 474 \item TomCyclic, 766 \item TomDihedral, 766 \item TomFrobenius, 767 \item TomMat, 761 \item TOS, 922 \subitem features, 927 \subitem installation, 923 \subitem options, 927 \item total length of a presentation, 474 \item Trace, 245 \subitem for algebraic extensions, 394 \subitem for gaussians, 378 \item trace \subitem of a field element, 245 \item Trace for MeatAxe matrices, 1079 \item TraceMat, 619 \item TransferDiagram, 849 \item TransformingPermutations, 806 \item TransformingPermutationsCharTables, 806 \item TransitiveGroup, 638 \item TransitiveIdentification, 638 \item Transitivity, 324 \item Transposed for MeatAxe matrices, 1079 \item TransposedMat, 618 \item TreatAsPoly, 1010 \item TreatAsVector, 1009 \item tree decoding, 485 \item TriangulizeMat, 620 \item TrivialSubalgebra, 672 \item TrivialSubgroup, 263 \item Tuples, 748 \item TwoGroup, 641 \item TwoSquares, 379 \item type \subitem algebraic elements, 392 \subitem boolean, 725 \subitem cyclotomic, 365 \subitem gaussian integers, 375 \subitem gaussian rationals, 375 \subitem integer, 343 \subitem list, 553 \subitem matrices, 615 \subitem rationals, 361 \subitem records, 729 \subitem strings, 587 \subitem words, 451 \item TzEliminate, 476 \item TzFindCyclicJoins, 478 \item TzGo, 475 \item TzGoGo, 476 \item TzPrint, 468 \item TzPrintGenerators, 467 \item TzPrintLengths, 482 \item TzPrintOptions, 482 \item TzPrintPairs, 482 \item TzPrintPresentation, 468 \item TzPrintRelators, 467 \item TzPrintStatus, 467 \item TzSearch, 477 \item TzSearchEqual, 478 \item TzSubstitute, 478 \item TzSubstituteCyclicJoins, 482 \indexspace \item ULTRIX, 907 \item Unbind, 739 \item UnderlyingGraph, 997 \item UndirectedEdges, 988 \item Union, 218 \item union \subitem of boolean lists, 583, 584 \subitem of domains, 218 \subitem of sets, 577, 579 \item UnionBlist, 583 \item UnionCode, 1042 \item UnitalAlgebra, 664 \item UnitalSubalgebra, 666 \item UniteBlist, 584 \item UniteSet, 577 \item Units, 228 \subitem for gaussians, 378 \item UNIX \subitem features, 912 \subitem installation, 908 \subitem options, 912 \item Unknown, 400 \item Unknowns, 399 \item UnorderedTuples, 747 \item until, 189 \item UpdateMap, 848 \item Upgrading GAP, 903 \item UpperBound, 1061 \item UpperBoundElias, 1060 \item UpperBoundGriesmer, 1061 \item UpperBoundHamming, 1059 \item UpperBoundJohnson, 1060 \item UpperBoundMinimumDistance, 1062 \item UpperBoundPlotkin, 1060 \item UpperBoundSingleton, 1059 \item UpperCentralSeries, 268 \subitem for character tables, 779 \item Using the MeatAxe in GAP. An Example, 1075 \item Using Vector Enumeration with the MeatAxe, 1121 \item UUVCode, 1041 \indexspace \item Value, 418 \item ValueMolienSeries, 822 \item Variables, 183 \item Vector Enumeration, 1115 \item Vector Enumeration Package, 958 \item Vector Space Functions for Algebras, 670 \item Vector Space Functions for MeatAxe Modules, 1083 \item Vector Space Records, 338 \item Vector Spaces, 337 \item VectorCodeword, 1009 \item Vectors, 597 \item VectorSpace, 337 \item VEInput, 1116 \item VEOutput, 1116 \item Vertex-Colouring and Complete Subgraphs, 1000 \item VertexColouring, 1001 \item VertexDegree, 986 \item VertexDegrees, 986 \item VertexName, 986 \item VerticalConversionFieldMat, 1067 \item Vertices, 986 \item VirtualCharacter, 885 \indexspace \item WedgeGMod, 1098 \item Weight, 517 \item WeightCodeword, 1011 \item WeightDistribution, 1049 \item WeightHistogram, 1071 \item WeightsTom, 760 \item Weyl, 1133 \item Weyl Groups and Hecke Algebras, 1123 \item Weyl Package, 960 \item WeylClassPolynomials, 1140 \item WeylConjugacyClasses, 1136 \item WeylCosetPermRepresentation, 1136 \item WeylElements, 1136 \item WeylLengthPerm, 1134 \item WeylMueMat, 1138 \item WeylReflections, 1135 \item WeylRightCosetRepresentatives, 1135 \item WeylWordPerm, 1134 \item While, 189 \item while, 189 \item while loop, 189 \item Whitespaces, 181 \item WholeSpaceCode, 1030 \item Why Group Characters, 879 \item Windows, 914 \subitem installation, 916 \item WordLength, 1047 \item words, 451 \item Words in Abstract Generators, 451 \item Words in Finite Polycyclic Groups, 489 \item wreath product \subitem character table, 789 \item WreathPower, 1099 \item WreathProd, 1098 \item WreathProduct, 303 \subitem for ag groups, 504 \item WreathProduct for Ag Groups, 508 \item WreathProduct for Groups, 304 \indexspace \item X, 413 \indexspace \item Z, 403 \item ZClassRepsDadeGroup, 656 \item Zero and One for Algebras, 669 \item Zero and One for Matrix Algebras, 686 \item ZumbroichBase, 386 \end{theindex}